Attenuation of Nonlinear Waves by Rigid Vegetation: Comparison of Different Wave Theories

Abstract

This study investigates the performances of theoretical wave attenuation models in predicting vegetation-induced wave decay. The existing theoretical models are all based on linear wave theory, which cannot describe nonlinear waves accurately. This study applies Stokes second-order and cnoidal wave theories to solve the energy balance equation for wave height evolution. Results from a phase-resolving numerical model serve as reference solutions. A total of 30 tests are devised for shallow-intermediate water waves through emergent and submerged vegetation. The differences between theoretical and numerical model results (ϵH) and between linear and nonlinear-based theoretical model results (ΔH) are quantified. The test results show that for wave propagation through emergent vegetation ΔH is ≤6% and ϵH is ≤5%, whereas over submerged vegetation, ϵH reaches as large as 25%. With a 5% tolerance of ϵH, linear-based theoretical models remain valid for emergent cases and submerged cases with a small Ursell number (≤30 in this study). This work has found that the inability of theoretical models to simulate the in-canopy velocity reduction and nonlinear wave-wave triad interactions contributes to the large ϵH in submerged cases.